C a v i t a t i o n o f

H y d r a u l i c M a c h i n e r y

H Y D R A U L I C M A C H I N E R Y B O O K SERIES

- Hydraulic Design of Hydraulic Machinery Editor: Prof H Radha Krishna

- Mechanical Design and Manuíacturing of Hydraulic Machinery

Editor: ProỊ Mei z Y - Transỉent Phenomena of Hydraulic Machinery

Editors: Prof s Pejovic, Dr A p Boldy - Cavitation of Hydraulic Machinery

Editor: Proị Li s c - Erosion and Corrosion of Hydraulic Machinery

Editors: ProỊ Duan c G, ProỊ V Karelin - Vibration and Oscillation of Hydraulic Machinery

Editor: PTOỊ H Ohashi - Control of Hydraulic Machinery

Editor: ProỊ H Brekke The International Editorial Committee (IECBSHM): Chairman: ProỊ Duan c G Treasurer: Dr R K Turton Committee Members: ProỊ H Brekke (Norway) ProỊ E Egusquiza (Spain) Dr H R Graze (Australia) ProỊ p Henry (Switzerland). ProỊ V Kareíin (USS) ProỊ Li Sheng-cai (China) ProỊ M Tadeu de Almeida (Brazil) ProỊ M Matsumura (Japan) ProỊ Ả Mobarak (Egypt) ProỊ H Netsch (Canada) Prof s Peịovic (Yugoslavia) ProỊ H Petermann (Germany) ProỊ c s Song (USA) ProỊ Hans Ingo Weber (Brazil) Honorary Members: Prof B Chaiz (Switzerland)

Secretary: ProỊ Li s c DĩÁP Boldy

Proị V p Chebaevski (USS) ProỊ M Fanelli (Italy) ProỊ R Guarga (Uruguay) Dr H B Horlacher (Germany) ProỊ G Krịvchenko (USS) ProỊ Liu ỏ K (China) PTOỊ c s Marùn (USA) ProỊ Mei Zu-yan (China) ProỊ H Murai (Japan) ProỊ H Ohashi (Japan) ProỊ D Perez-Franco (Cuba) ProỊ H c Radha Krishna (India) ProỊ c Thirriot (Prance) ProỊ G Ziegler (Austria) PTOỊ J Raabe (Germany)

^ ị p SERIES ÔN HYDRAULIC MACHINERY - VOL.1 Committee Chairman: c. G. Duan Series Editor: s. c. Li

Cavitation of

Hydraulic Machinery

E d i t o r

s. c. Li University oi Warwick, U.K.

Imperial College Press

Published by Imperial College Press 57 Shelton Strèet Covent Garden London WC2H 9HE Distributed by World Scìentific Publishing Co. Pte. Ltd. p o Box 128, Farrer Road, Singapore 912805 USAọỊpce: Suite 1B, 1060 Main Street, RiverEdge, NJ 07661 UK offìce: 57 Shelton Strcet, Covent Ganíen, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue rccorđ for this book is avaìlable from the British Library.

CAVITATION OF HYDRAULIC MACHINERY Copyright © 2000 by Imperial College Press AU rìghts reserved. This book, ÓT parts thereo/. may noi be reproduced in anyform or hy any means. elecíronic ÓT mechanicaỉ, including photocopying, recordìng ÓT any in/ormation storage and retrievaì system now known or to be invented, without writĩen permissionfrom the Publisher.

For photocopying of material in this volume, please pay a copying fee ihrough the Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy ìs nót required from the publisher.

ISBN 1-86094-257-1

Printed in Singapore by Ưto-Print

C O N T E N T S

References 3 Bubble Dynamics

Part 1: Single Bubble A Shima

3.1 Rayleigh Analysis 3.1.1 Besant's Problem

xui XV xix Ì

Preface Foreword of the Editor Contributing Authors Ì Introduction

s c Li 1.1 Cavitation Ị

1.1.1 Discovery 1.1.2 ClassiScation

1.2 Hydraulic Machinery and Cavitation 3

1.2.1 Problems Caused by Cavitation 3

1.2.2 Combating Cavitation Reíerences

2 Cavitation and Cavitation Types A J Acosta

2.1 Cavitation Phenomenon 2.1.1 Cavitation 2.1.2 Hydrodynamic Cavitation

2.2 Types oi Cavitation 2.2.1 Cavitation Index 2.2.2 Scale ESects and Cavitation Types 12

2.3 Cavitation Eữects 2.3.1 General Phenomena 2.3.2 InAuences ôn Machine Períormance 25 2.3.3 System Stability

2.4 Cavitation Nucleation and Inception 2.4.1 Inception 2.4.2 Nuclei Measurement 2.4.3 Concluding Remarks 3 8

40

5

24 24

28 30 30

47 47

47 47

V

vi Contents

3.1.2 Rayleigh's Solution 48 3.2 Vaporous and Gaseous Bubbles 49

3.2.1 Classiíìcation 49 3.2.2 Stability 49

3.3 Viscosity and Compressibility Eíĩects 50 3.3.1 Eíĩects of Viscosity and Suríace Tension 50 3.3.2 Compressibility Eữect 50

3.4 Bubble Rebound 53 3.4.1 Introduction 53 3.4.2 Studies of Rebound 53

3.5 Nonspherical Collapse and Micro-jet Formation 54 3.5*1 Collapse near Solid Wall 54 3.5.2 Collapse in Contact with Solid Wall 55

3.6 Pressures Generated át Collapse 57 3.6.1 Impact Pressure and Their Modes 57 3.6.2 Temperature Effect 60

Reíerences 61 Part 2: Multi-Bubbles (stochastic Behaviour) 65

s c Li 3.7 Origins oi Bubble Stochasticity 65

3.7.1 Introduction 65 3.7.2 Bubble-Boundary Interaction 67 3.7.3 Bubble-Bubble iioteraction 73 3.7.4 Bubble-Flow Field Interaction 94 3.7.5 Remarks 115

3.8 Stochastic Models oi Cavitation Bubbles 117 3.8.1 Introduction 117 3.8.2 Single-Event Model 117 3.8.3 Muĩti-Event (Cluster) Model 118 3.8.4 Comprehensive Model 120

3.9 Power Spectrum 121 3.9.1 Introduction 121 3.9.2 Spectrum of Single-Bubble Collapse 121 3.9.3 Spectrum for Sequence of Single Events 127 3.9.4 Spectrum for Sequence of Clusters 137 3.9.5 Spectrum for Comprehensive Sequence 148

Reíerences 153 157

Contents vii

4 Cavitating Plow 4.1 General Features 157

H Murai 4.1.1 Sheet Cavitation 157 4.1.2 Travelling Bubble Cavitation 160 4.1.3 Vortical Cavitation 161 4.1.4 Hydraulic Loss Caused by Cavitation 161

4.2 Hydroíoil and Hydroíoil Cascade 166 H Murai

4.2.1 Cavitation Characteristics of Hydroíoil 166 4.2.2 Cavitation Characteristics of Conventional

Airíoil Sections 170 4.2.3 Cavitation Characteristics of Ogival Hydroíoils 171 4.2.4 Cavitation Characteristics of Hydroíoil Cascade 175 4.2.5 Cavitation Characteristics of Conventional Airíoil

and Ogival Proíiles 176 4.2.6 Hydroíoil Proíìle Suitable for Decelerating

and Accelerating Cascades 180 4.2.7 Computer Simulation oi Partially Cavitating Foil 182 4.2.8 Supercavitating Hydroíoil 184 4.2.9 Supercavitating Hydrofoil Cascade 186

4.3 Control vâlves 187 E Outa

4.3.1 General Features oi Control Valve Cavitation 187 4.3.2 Cavitation Pictures of Globe Valve Flows 194 4.3.3 Cavitation Inception due to Vortex Growth 197 4.3.4 Cavitation Erosion and Anti-Cavitation Valves 202

References 205 5 Cavitation Phenomena in Hydraulic Machinery 211

5.1 General Features of Turbine Cavitation 211 H Tanaka

5.1.1 Cavitation in Prancis Turbines 211 5.1.2 Cavitation in Propeller Turbines 220 5.1.3 Cavitation in Pelton Turbines 225 5.1.4 Cavitation in Prancis Pump-Turbines 226

5.2 General Features of Pump Cavitation 229 R K Turton

5.2.1 Introduction 229 5.2.2 General Eíĩect ôn Pumps 229

viii Contents

5.2.3 Nét Positive Suction Head 232 5.2.4 Definition of Critical NPSHR 235 5.2.5 Implications for Pump Design 236 5.2.6 The Role of the Inducer 240

5.3 Pump Cavitation Similarity 242 V Chebaevsky and V Petrov

5.3.1 Problem Nature and Similarity Conditions 242 5.3.2 Thermodynamic Property Simulation 248

5.4 Cavitatiou Detection Techniques 251 E Egusquiza

5.4.1 Introduction 251 5.4.2 Generation of Noise and Vibration 252 5.4.3 Propagation 253 5.4.4 Background Noise 254 5.4.5 Cavitation Detection in Prequency Domain 255 5.4.6 Cavitation Detection in Time Domain 259 5.4.7 Cavitation Detection with Time-Prequency Analysis 263

Reíerences 265 6 Cavitation Damage to Hydraulic Machinery 269

6. Ì General Mechanism of Cavitation Damage 269 Y Iwai and T Okada

6.1.1 Introduction 269 6.1.2 Cavitation Bubble Collapse Pressures and Damage 269 6.1.3 Correlation between Erosion Resistance

and Mechanical Property 276 6.2 Cavitation Damage in Turbines 277

s c Li 6.2.1 Introduction 277 6.2.2 Propeller and Kaplan Turbines 285 6.2.3 Prancis Turbine 286 6.2.4 Pelton Turbine 290 6.2.5 Cavitation Guarantee 292

6.3 Cavitation Damage in Pumps 295 s c Li

6.3.1 Introduction 295 6.3.2 Axial Flow Pumps 295 6.3.3 Centriíugal Pumps 296 6.3.4 Pump-turbines 298

Contents ix

6.3.5 Cavitation Guarantee 299 6.4 Silt-Laden Water EfFect 302

s c Li 6.4.1 Introduction 302 6.4.2 Silt Erosion 302 6.4.3 Synergism of Silt and Cavitation Erosions 307

6.5 High Resistance Materials 314 s e n

6.5.1 Introduction 314 6.5.2 Fused Materials 314 6.5.3 Non-fused Materials 330

6.6 Repair oi Machine 334 s c Li

6.6.1 Introduction 334 6.6.2 Cause of Damage 334 6.6.3 Main Concerns in Repair 336 6 6 4 Examples 343

References 353 7 Cavitation Caused Vibrations 359

7.1 Cavitation Pressure Pulsation in Turbines 359 7.1.1 Blade Cavity Pulsations 359

J Sato 7.1.2 Blade Wake Cavitation Pulsations 364

J Sato 7.1.3 Draft Tube Vortex Core Cavitation Pulsations 364

p Henry 7.2 Cavitation Induced Pulsations in Pumps 369

7.2.1 Introduction 369 R K Turton

7.2.2 Characteristics oi Cavitation Induced Pulsations 372 Y Tsujimoto

7.2.3 Mechanisms of Cavitation Induced Pulsations 376 Y Tsvýimoto

7.2.4 Cavitation Characteristics - Mass Flow Gain Factor and Cavitation Compliance 380

Y Tsujimoto 7.3 InAuence of Operating Conditions 383

p Henry

X Contents

7.3.1 Preliminary Discussion 383 7.3.2 Part Load Precession 383 7.3.3 80% Load Oscillations 388 7.3.4 Draft Tube Free Oscillations 388 7.3.5 Auto-oscillations 398 7.3.6 InAuence oi the Test Head 401 7.3.7 Thoma Number 403

7.4 Cavitation Resonance in Hydraulic Machinery Installations 405 p Henry

7.4.1 Introduction 405 7.4.2 Prototype Installation 405 7.4.3 Model Tests 409 7.4.4 Stability of the Prototype Installation 413

References 417 8 Unsteady Cavitation Flows Caused by Machine Transients 423

Part 1: Turbine Transients 423 c s Martin

8.1 Introduction 423 8.2 Types of Turbine Cavitation 424

8.2.1 Prancis Turbines 424 8.2.2 Kaplan Turbines 432

8.3 Draft-Tube Column Separation Incidents 433 8.4 Physical Modelling of Cavitating Transient Flows 436 8.5 Two-Phase Flow Modelling in Conduits 440

8.5.1 Acoustic Velocity 441 8.5.2 Slug Flow 444

8.6 Analytical Modelling oi Cavitating Transient Flows 444 Reíerences 445

Part 2: Pump Transients 451 H Tsukamoto

8.7 Introduction 451 8.8 Transient Cavitation in Discharge Lines 451

8.8.1 Transient Cavitation Type 451 8.8.2 Water Column Separation 453

8.9 Transient Cavitating Flow in Turbopumps 453 8.9.1 True Total Pressure Rise 453 8.9.2 Transient Behaviour of a Cavitating Pump 455 8.9.3 Transient Characteristics of Pump 457